DESCRIPTION (adapted from the Abstract): Hierarchical models enable the combining of information from similar and independent experiments, yielding improved estimation of both individual and shared model characteristics. Many data sets arising from AIDS clinical trials offer ideal settings for this type of synthesis. This application is focused on developing the necessary hierarchical modeling methods for improved analysis of such datasets, as well as corresponding user-friendly computing tools to enable use of the methods by non-expert statistical support staff at clinical trial data coordinating centers. After a brief review of several past developments, three areas specific to the health sciences are proposed for in-depth exploration. First, the interim monitoring of AIDS clinical trials data is shown to be a fruitful area of application. A fully hierarchical Bayesian approach to this problem specifies the likelihood and prior distributions with appropriate loss functions. The researchers will compare the traditional analytic method, backward induction, with a forward sampling algorithm that substantially eases the analytic and computational burden. A second area for investigation is the use of hierarchical models for highly stratified survival data. A fully parametric approach (a proportional hazards, Weibull baseline hazard model) emerges as easily interpretable, while permitting a high degree of model flexibility. The researchers will also consider a semiparametric model which is more flexible, but somewhat more difficult to specify and interpret. A third area proposed for study is the analysis of data arising from several AIDS trial protocols in process simultaneously at a number of clinical units. Here, hierarchical modeling is ideal for combining information to obtain improved estimates of both study- and unit-specific model parameters. The NIAID-sponsored Community Programs for Clinical Research on AIDS (CPCRA), coordinated at the University of Minnesota, will provide a wealth of data on which to evaluate these hierarchical methods. The three specific proposed problem areas are not intended to be exhaustive, but rather indicative of the broad issues which underlie all AIDS clinical trial analyses, and the inevitable future stream of opportunities for combining hierarchical modeling theory with AIDS research application.